Question: Solve for $x$ and $y$ using elimination. ${-x-4y = -6}$ ${x-5y = -3}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-9y = -9$ $\dfrac{-9y}{{-9}} = \dfrac{-9}{{-9}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-x-4y = -6}\thinspace$ to find $x$ ${-x - 4}{(1)}{= -6}$ $-x-4 = -6$ $-x-4{+4} = -6{+4}$ $-x = -2$ $\dfrac{-x}{{-1}} = \dfrac{-2}{{-1}}$ ${x = 2}$ You can also plug ${y = 1}$ into $\thinspace {x-5y = -3}\thinspace$ and get the same answer for $x$ : ${x - 5}{(1)}{= -3}$ ${x = 2}$